Given that f -x-is a differentiable of x and that f-x- - f -y- - f -x- - f -y- - f -xy- -2 and thatf -2- -5-Then f -3- is equal to-6241519

Question

Given that f -x-is a differentiable of  x and that f-x- - f -y- - f -x- - f -y- - f -xy- -2 and thatf -2- -5-Then f -3- is equal to-6241519

Toppr Admin · Accepted Answer

Given- f-x-f-y-f-x-f-y-f-xy-x2212-2-x2212-1-f-2-5f-x-x2-1Equation 1-x21D2-xA0-x2-1-y2-1-x2-1-y2-1-x2y2-1-x2212-2x2y2-x2-y2-1-x2-y2-x2y2-1-x2234-f-3-x2-1-32-1-10

Given that $f (x)$
is a differentiable function of $x$ and that $f (x)$ . $f (y)$ = $f (x)$ + $f (y)$ + $f (x y) - 2$ and that
$f (2) = 5$ .
Then $f (3)$ is equal to?

$6$
$24$
$15$
$19$

Given, $f (x) . f (y) = f (x) + f (y) + f (x y) - 2 - (1)$
$f (2) = 5$
$f (x) = x^{2} + 1$
Equation $1 \Rightarrow$ $(x^{2} + 1) (y^{2} + 1) = x^{2} + 1 + y^{2} + 1 + x^{2} y^{2} + 1 - 2$
$x^{2} y^{2} + x^{2} + y^{2} + 1 = x^{2} + y^{2} + x^{2} y^{2} + 1$
$∴ f (3) = x^{2} + 1 = 3^{2} + 1 = 10$

Given that f(x)is a differentiable function of x and that f(x) . f(y) = f(x)+ f(y) + f(xy)−2 and thatf(2)=5.Then f(3) is equal to?6241519

Given, f(x).f(y)=f(x)+f(y)+f(xy)−2−(1)f(2)=5f(x)=x2+1Equation 1⇒ (x2+1)(y2+1)=x2+1+y2+1+x2y2+1−2x2y2+x2+y2+1=x2+y2+x2y2+1∴f(3)=x2+1=32+1=10

Given that $f (x)$
is a differentiable function of $x$ and that $f (x)$ . $f (y)$ = $f (x)$ + $f (y)$ + $f (x y) - 2$ and that
$f (2) = 5$ .
Then $f (3)$ is equal to?

$6$
$24$
$15$
$19$

Given, $f (x) . f (y) = f (x) + f (y) + f (x y) - 2 - (1)$
$f (2) = 5$
$f (x) = x^{2} + 1$
Equation $1 \Rightarrow$ $(x^{2} + 1) (y^{2} + 1) = x^{2} + 1 + y^{2} + 1 + x^{2} y^{2} + 1 - 2$
$x^{2} y^{2} + x^{2} + y^{2} + 1 = x^{2} + y^{2} + x^{2} y^{2} + 1$
$∴ f (3) = x^{2} + 1 = 3^{2} + 1 = 10$